We've all been told this before and I know various diseases can be detected by looking inside the eye but how exactly?? Structural changes within the eye, such as the veins, colour changes?? any suggestions?

In addition to jaundice/icterus, some other information of various (non-eye) diseases can be seen by looking in the eyes: retinopathy, for example, can indicate conditions such as advanced diabetes or hypertension. Furthermore, the state of consciousness and be evaluated by pupil reactions to light. Increase in the intra-cranial pressure can also be seen in the eye and so forth.

Generally, though, it is quite limited what we can see by looking someone in the eyes alone.

Visualization using an opthalmoscope allows you to see the structures in the ocular fundus - optic disc, retinal vessels, general background and macula. Abnormalities in these areas can give you insight into different disease states. (I'm not sure if you want details about that). The retinal vessels themselves, the only place in the body where you can view your blood vessels directly.

Not only that, the movement of the eyes is actually controlled by different cranialnerves (III, VI, IV), so if your eyes won't turn in a certain direction, will be indicative of a paralysis to that specific cranial nerve.

I would feel more optimistic about a bright future for man if he spent less time proving that he can outwit nature and more time tasting her sweetness and respecting her seniority. ~ E. B. White